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Neither means percentage. Percentage is one hundred times ratio or rate. The Japanese word for it is 百分率. Likewise, permillion is one million times ratio or rate. The Japanese word for it is 百万分率.

My impression is that 割合 and ratio are the general terms for a quantity divided by another quantity (usually but not always of the same dimension). 率 and rate are especially for cases where its lowness or highness is connected to its preferred amount in an ideal situation. For example, 率 or rate is used for 誤差~ or error ~ because the ideal case would be zero. It can be also used for 正解~ or correctness ~ because the ideal situation will be one. It is also used in 転送~ or bit ~ because the larger the better.

率 is often used after a sort of noun in order to express the percent of ...;for instance percentage "百分率", percent of pass "合格率", percent of attendance "出勤率" etc.
and as mentioned above, when use with "比" as"比率", 比率shall substitute "割合".